Approximate and exact nodes of fermionic wavefunctions: Coordinate transformations and topologies

Michal Bajdich, Lubos Mitas, Gabriel Drobný, Lucas K. Wagner

Research output: Contribution to journalArticlepeer-review


A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with s,p,d one-particle orbitals is presented. We find exact nodes for some cases of two-electron atomic and molecular states and also the first exact node for the three-electron atomic system in S4 (p3) state using appropriate coordinate maps and wave function symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into three-dimensional space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wave functions.

Original languageEnglish (US)
Article number075131
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number7
StatePublished - Aug 15 2005
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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